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Wed, 11 Aug 2010 14:09:27 +0200Wed, 11 Aug 2010 14:09:27 +0200Equivariant character bijections in groups of Lie type https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2229
A classical conjecture in the representation theory of finite groups, the McKay conjecture, states that for any finite group and prime number p the number of complex irreducible characters of degree prime to p is equal to the number of complex irreducible characters of degree prime to p of the normalizer of a p-Sylow subgroup. Recently a reduction theorem was proved by Isaacs, Malle and Navarro: If all simple groups are “good”, then the McKay conjecture holds. In this work we are concerned with the problem of goodness for finite groups of Lie type in their defining characteristic. A simple group is called “good” if certain equivariant bijections between the involved character sets exist. We present a structural approach to the construction of such a bijection by utilizing the so-called “Steinberg-Map”. This yields very natural bijections and we prove most of the desired properties.Johannes Maslowskidoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2229Wed, 11 Aug 2010 14:09:27 +0200